With a files explorer, browse to your Modelio workspace directory (by default it is c:\Users\yourLogin\modelio\workspace in Windows or /home/yourLogin/modelio/workspace in Linux). In this directory, you can find a list of directories. Each directory is a modelio project.

You can clone a project, just by copying the directory (with all its contents) to another directory.

Each model element in Modelio is assigned at creation an UUID that identifies it universally.

If a second user use a "backup clone" of the project, the existing model elements
will keep their original identifier and will be seen by Modelio as the same object.
If you happen to merge the both projects later by a way or another (Model component, SVN, ...) you will encounter serious problem such has "Duplicate objects" errors or model objects overwriting original ones.

The "import model" contextual command imports a "copy" of the model so that imported element identifiers are different that the original model.
Another effect is that you may run many times the "import model" command to
make many copies of the original model in the same project.

I need to make a new project that is an _exact_ copy of an existing project except for the project name. The above doesn't work in Modelio 3.7. I've also tried saving a copy of the existing project under a new name. However, the old name still shows up in the copy and can't be changed.
Any help

Thanks. I got it to work. I run Linux and the path had to be entered as "<path to home directory>/modelio/workspace/Project1/p". If I omit the final p or type the whole project.conf I still get the file-does-not-exist error.
p.s. Just did some more testing. It seems that placing a space after the final / in the path also works.